Interest in computing ultrasonic images from scattering data taken over many views has been stimulated by the clinical utility of systems that employ x-rays to produce tomograms from a number of projections. However, analogous ultrasonic methods based on simplifying assumptions that usually neglect multiple scattering effects have not yielded satisfactory quantitative images. Success, nevertheless, appears now possible because limitations of available imaging methods are better understood, new ultrasonic instrumentation has been developed, progress in the theory of inverse scattering has been made, and computing expertise as well as suitable hardware facilities are available for the solution of relevant large scale optimization and computing problems. This research utilizes data measured using a unique ring transducer system. The system permits transmit waveforms to be individually programmed, synthesis of arbitrary transmit and receive apertures, and alteration of transmit beams as well as receive focussing for iterative reconstruction. A new method of image reconstruction that uses eigenfunctions of the scattering operator has been developed. The method expresses the solution of the full nonlinear problem as an expansion in products of retransmitted fields defined in terms of the eigenfunctions. Progress has included compensation of transducer aberrations, high-resolution compound b-scan imaging, adaptive adjustment of gain, design of prescribed pulse wavefronts, development of an efficient solver for forward problems, and experience with measurements as well as computations for simple test objects. Overall, a strategy using eigenfunction analysis and optimization is being pursued to reconstruct images from measurements of scattering. Further studies will involve additional development of the current forward problem solver, measurements of scattering produced by larger and more complicated test objects, and continued development of the present image reconstruction method using eigenfunctions. Success in this research would significantly extend ultrasonic capabilities particularly in the area of breast imaging.